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August, 1975 Entropy Zero $\times$ Bernoulli Processes are Closed in the $\bar d$-Metric
Paul Shields, J.-P. Thouvenot
Ann. Probab. 3(4): 732-736 (August, 1975). DOI: 10.1214/aop/1176996314

Abstract

An entropy zero $\times$ Bernoulli process is a stationary finite state process whose shift transformation is the direct product of an entropy zero transformation and a Bernoulli shift. We show that the class of such transformations which are ergodic is closed in the $\bar{d}$-metric. The $\bar{d}$-metric measures how closely two processes can be joined to form a third stationary process.

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Paul Shields. J.-P. Thouvenot. "Entropy Zero $\times$ Bernoulli Processes are Closed in the $\bar d$-Metric." Ann. Probab. 3 (4) 732 - 736, August, 1975. https://doi.org/10.1214/aop/1176996314

Information

Published: August, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0333.28007
MathSciNet: MR385072
Digital Object Identifier: 10.1214/aop/1176996314

Subjects:
Primary: 28A65
Secondary: 60G10

Keywords: $\bar d$-metric , Bernoulli shift , entropy zero

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 4 • August, 1975
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